AMU Engineering 2018 solved paper Solved Paper

According to the question,
Given, mass of the particle =m ∴ Linear momentum of the particle, p=mv
or =mv

^

i

Position of particle at time t,r=x

^

i

+y

^

j

=vt

^

i

+y

^

j

‌‌‌‌(∵x=vt)
∴ Angular momentum of the particle about O.
L=r×p=(vt

^

i

+y

^

j

)×mv

^

i

L=|

^ i	^ j	^ k
vt	y	0
v	0	0

|
L=

^

i

(0−0)−

^

j

(0−0)+

^

k

(0−vy)
=−vy

^

k

( constant )
(∵ Particle is moving in +ve x -direction.)
Hence, angular momentum of particle w.r.t the origin remains constant for all positions of the particle.